You may wish to review the Error Analysis portion of the Prelab for Physics 2212 Lab #8, Capacitance and RC Circuits.

You are watching: What does the slope of a force vs current graph represent The magnetic force, F, on a current-carrying wire

F = IL×BorF = ILB sinθ

depends on the current through the wire, I, the length of wire in the magnetic field,L, the magnitude of the magnetic field, B, and, since L andB are vectors, the angle θ between the length of wire and thefield. The accompanying illustration of this relationship is a perspective sketch—note that L and B define a plane, and F must beperpendicular to that plane. The direction of (conventional) current defines the direction ofpositive L. This relationship will be examined two ways. First, a constant current will be selected, andwires of various lengths will be placed perpendicular to a magnetic field (θ=90°).The force magnitude will be measured. A graph of the force as a function of length should yield a straightline of slope IB. Since I is known, the magnitude of the magnetic field can be calculated.

Next, a particular wire length will be selected and placed perpendicular to a magnetic field (θ=90°). Various currents will be passed through the wire, and theresulting force magnitude will be measured. A graph of the force as a function of current shouldyield a straight line of slope LB. Since L is known, the magnitude of the magneticfield can be calculated.

These two measures of the magnetic field magnitude can be compared to each other.

### Measuring the Force

Experimental Technique: An obvious way to do this experiment is to put a wire into the field of a permanent magnet, passcurrent through the wire and measure the force on the wire. Then one can vary the length, the currentand the angle to check out everything in the law. There are two problems with this. First its difficultto measure a force on a rigid wire (there will be current leads and other stuff hanging on it whichconfuses matters). Secondly the leads connected to the sample wire might also experience part of themagnetic field and this produces forces which may confuse matters. The experiments we have designed foryou overcome both of these things easily.

Measuring the Force: Consider first figure above; the force is on the wire which in this case is up. Let us assumethat the magnetic field is produced by a horseshoe magnet. Newton"s Third Law tells us theremust be an equal an opposite force downward on the magnet. Instead of measuring theforce on the wire, we could just as well measure the force on the magnet. This is what wedo by placing the magnet on the pan of a scale and measuring force as an apparent weight.

An equal arm balance is illustrated below. Initially the magnet is placed on the pan and a massM added to the other pan to restore equilibrium. Obviously M would be the mass of themagnet and the force of gravity on the magnet would be its weight, Mg. The wire is in thejaws of the magnet and suspended rigidly from a stand which sits on the bench (it does nottouch the magnet or scale). Now we send current through the wire. There will be a force F on the wire (let usassume up) and therefore a force of reaction on the magnet (down) causing the magnet panto go down, just as though additional mass had been placed on that pan. We now addadditional mass m to the mass pan and restore equilibrium. The gravitational forceon the additional mass m is mg, and that exactly equals the force on the magnetwhich in turn is exactly equal to the force on the wire. Thus

F = mg = ILB sinθ

and we have our measurement of the force on the wire.

(Of course if the direction of the current in the wire were reversed then the force onthe wire would be down, the force on the magnet up, and to restore equilibrium a massm would need to be subtracted from the mass scale pan. That is an equallygood way of doing things.)

The balance we use in the lab is not actually an equal arm balance wheremasses need to be added or subtracted. Rather it is a variable arm type of balance where amass rider is moved along the mass arm until the torque on the mass arm(clockwise) balances the torque on the scale arm (counterclockwise). The variable arm has acalibrated scale marked on it so that the position of the rider tells you the actualmass on the scale pan. Wire Samples: These are made of a wide strip of metal deposited in the shape of a rectangularU on an insulating board (in fact a Printed Circuit or PC board). This isplaced in the magnetic field, as shown, so that the connecting central leg of theU is entirely in the field. It is on this piece of the wire that we wish tomeasure force and the force will be either up or down (depending on the currentdirection).

What about forces on the legs to the left and right which act asleads to convey the current to the wire? These legs will be partly in the magneticfield and experience some force. Make sure you can think of at least one reason whythey do not matter.

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The wires are wide (about two mm). Think about whether you should measure the outerlength (to outside the legs), the inner length (to inside of the legs), or something else.